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Bioinformatics Advance Access published online on May 30, 2007
Bioinformatics, doi:10.1093/bioinformatics/btm278
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© The Author (2007). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Computational methods for diffusion-influenced biochemical reactions

Maciej Dobrzynski a,*, Jordi Vidal Rodríguez b, Jaap A. Kaandorp a and Joke G. Blom a

aCWI (Center for Mathematics and Computer Science) Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
bSection Computational Science, Faculty of Science, University of Amsterdam Kruislaan 403, 1098 SJ Amsterdam, The Netherlands

*To whom correspondence should be addressed. Maciej Dobrzynski, E-mail: m.dobrzynski{at}cwi.nl


  Abstract

Motivation: We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics and the reactiondiffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in E. coli.

Results: In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the subvolumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems.

Availability: Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/.

Associate Editor: Dr. Jonathan Wren

Received on January 31, 2007; revised on April 20, 2007; accepted on May 17, 2007

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